log(6)(x+5)+log(6)x=2

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Solution for log(6)(x+5)+log(6)x=2 equation:


Simplifying
log(6)(x + 5) + log(6) * x = 2

Reorder the terms:
glo * 6(5 + x) + log(6) * x = 2

Reorder the terms for easier multiplication:
6glo(5 + x) + log(6) * x = 2
(5 * 6glo + x * 6glo) + log(6) * x = 2
(30glo + 6glox) + log(6) * x = 2

Reorder the terms for easier multiplication:
30glo + 6glox + 6glo * x = 2

Multiply glo * x
30glo + 6glox + 6glox = 2

Combine like terms: 6glox + 6glox = 12glox
30glo + 12glox = 2

Solving
30glo + 12glox = 2

Solving for variable 'g'.

Move all terms containing g to the left, all other terms to the right.

Reorder the terms:
-2 + 30glo + 12glox = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 30glo + 12glox = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 15glo + 6glox) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + 15glo + 6glox)' equal to zero and attempt to solve: Simplifying -1 + 15glo + 6glox = 0 Solving -1 + 15glo + 6glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 15glo + 1 + 6glox = 0 + 1 Reorder the terms: -1 + 1 + 15glo + 6glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 15glo + 6glox = 0 + 1 15glo + 6glox = 0 + 1 Combine like terms: 0 + 1 = 1 15glo + 6glox = 1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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